Determine the value of c so that each of the following functions can serve as a probability distribution of the discrete random variable X:

(a) f(x) = c(x^2 + 4) for x=0,1,2,3;
(b) f(x) = c(2,x)(3,3-x) for x=0,1,2

Solution:

a)

x 0 1 2 3

f(x) 4 5 8 13


F(0) = f(0) = 4
F(1) = f(0) + f(1) = 4 + 5 = 9
F(2) = f(0) + f(1) + f(2) = 4 + 5 + 8 = 17
F(3) = f(0) + f(1) + f(2) + f(3) = 4 + 5 + 8 + 13 = 30

how can I calculate c

and in the book answer is 1/30.


b)

=c(2+3,x+3-x)
=c(5,3)
=10

answer in book is 1/10

can anybuddy explain

∑f(x) =1

make summation of the functions f(0),f(1),f(2)...

then you can find c

sum f(x) =1